Fitting a binomial mixed logistic model with improved accuracy and computational efficiency

Simulation is used to demonstrate the advantage of a new procedure that utilizes the penalized quasi-likelihood (PQL) estimation of the variance components but improves the PQL estimation of the fixed effects via a method of conditional moments (MoCM) in the binomial mixed logistic model (BMLM). The BMLM is widely used for analyzing clustered data. While the PQL method has been traditionally used to avoid integration in the marginal likelihood function, it is known to introduce bias in the estimation. This study presents an unbiased estimation approach derived via the MoCM, assuming known variance components. When the latter are unknown, we show via extensive simulation studies that using the PQL estimators of the variance components, the proposed MoCM estimators of the fixed effects improve over the PQL estimators of the fixed effects in terms of both accuracy and computational efficiency.